1. Field of the Invention
The present invention relates to a two-element fθ lens of a micro-electro mechanical system (MEMS) laser scanning unit, and more particularly to a two-element fθ lens using an angular change varied with time in a sinusoidal relation for correcting a MEMS reflecting mirror having a simple harmonic motion to achieve a scanning linearity effect required by the laser scanning unit.
2. Description of the Related Art
At present, a laser scanning unit (LSU) used by a laser beam printer (LBP) controls a laser beam scanning by a high-speed rotating polygon mirror as disclosed in U.S. Pat. Nos. 7,079,171, 6,377,293 and 6,295,116 or TW Pat. No. I198966, and the principles of their operation are described below: a semiconductor laser emits a laser beam through a collimator and an aperture to form parallel beams. After the parallel beams pass through a cylindrical lens, the beams are focused at the width of the Y-axis in a sub scanning direction and along a direction parallel to the X-axis of a main scanning direction to form a line image and projected onto the high-speed rotating polygon mirror. The polygon mirror includes a plurality of continuous reflecting mirrors disposed substantially at or proximate to the focus position of the line image. The polygon mirror is provided for controlling the direction of projecting the laser beam, so that when a plurality of continuous reflecting mirrors are rotated at a high speed, the laser beam projected onto a reflecting mirror can be extended in a direction parallel to the main scanning direction (x-axis) at the same angular velocity and deviated from and reflected onto a fθ linear scanning lens. The fθ linear scanning lens is installed next to the polygon mirror and can be either a single-element lens structure (or a single scanning lens) or a two-element lens structure. The function of this fθ linear scanning lens is to focus a laser beam reflected by the reflecting mirror of the polygon mirror and projected onto the fθ lens into an oval spot that is projected onto a photoreceptor (or a photoreceptor drum, which is an image side) to achieve the requirement of the scanning linearity. However, the traditional laser scanning unit LSU still has the following drawbacks in its practical application:
(1) The manufacture of the rotating polygon mirror incurs a high level of difficulty and a high cost, and thus increasing the manufacturing cost of the LSU.
(2) The polygon mirror requires a high-speed rotation (such as 40000 rpm) and a high precision, and thus a cylindrical lens is required to be installed to the traditional LSU since the width of a general polygon mirror along the Y-axis of the reflecting surface of the mirror is very thin, so that the laser beams passing through the cylindrical lens can be focused to a line (or a spot on the Y-axis) and projected onto the reflecting mirror of the polygon mirror. This arrangement increases the number of components and also complicates the assembling operation procedure.
(3) The traditional polygon mirror requires a high-speed rotation (such as 40000 rpm), and thus the noise level is raised. Furthermore, the polygon mirror takes a longer time to accelerate from a starting speed to a working speed, and thus increasing the wait time of turning on the laser scanner.
(4) In the assembly of the traditional LSU, the central axis of a laser beam projected onto the reflecting mirror of the polygon mirror is not aligned precisely with the central rotating axis of the polygon mirror, so that it is necessary to take the off axis deviation of the polygon mirror into consideration to design the fθ lens, and thus making the design and the manufacture of the fθ lens more complicated.
In recent years, an oscillatory MEMS reflecting mirror is introduced to overcome the shortcomings of the traditional LSU assembly and replace the laser beam scanning controlled by the traditional polygon mirror. The surface of a torsion oscillator of the MEMS reflecting mirror has a reflecting layer for reflecting the light by oscillating the reflecting layer for the scanning. In the future, such arrangement will be applied in a laser scanning unit (LSU) of an imaging system, a scanner or a laser printer, and its scanning efficiency is higher than the traditional rotating polygon mirror. As disclosed in U.S. Pat. Nos. 6,844,951 and 6,956,597, at least one driving signal is generated, and its driving frequency is close to the resonant frequency of a plurality of MEMS reflecting mirrors, and the driving signal drives the MEMS reflecting mirror to produce a scanning path. In U.S. Pat. Nos. 7,064,876, 7,184,187, 7,190,499, US2006/0113393, or TW Pat. No. M253133, or JP Pat. No. 2006-201350, a MEMS reflecting mirror installed between a collimator and a fθ lens of a LSU module replaces the traditional rotating polygon mirror for controlling the projecting direction of a laser beam. The MEMS reflecting mirror features the advantages of small components, fast rotation, and low manufacturing cost. However, after the MEMS reflecting mirror is driven by the received voltage for a simple harmonic motion with a sinusoidal relation of time and angular speed, a laser beam projected on the MEMS reflecting mirror is reflected with a relation of reflecting angle θ and time t as follows:θ(t)=θs·sin(2π·f·t)  (1)
where, f is the scanning frequency of the MEMS reflecting mirror, and θs is the maximum scanning angle at a single edge after the laser beam passes through the MEMS reflecting mirror.
In the same time interval Δt, the corresponding variation of the reflecting angle is not the same but decreasing, and thus constituting a sinusoidal relation with time. In other words, the variation of the reflecting angle in the same time interval Δt is Δθ(t)=θs·(sin(2π·f·t1)−sin(2π·f·t2)), which constitutes a non-linear relation with time. If the reflected light is projected onto the target from a different angle, the distance from the spot will be different in the same time interval due to the different angle.
If the moving angle of the MEMS reflecting mirror is situated at a peak or a valley of a sine wave, the angular change will vary with time, which is different from the motion of a traditional polygon mirror at a constant angular velocity. If a traditional fθ lens is installed onto a laser scanning unit (LSU) of the MEMS reflecting mirror, the angular change produced by the MEMS reflecting mirror cannot be corrected, and the speed of the laser beams projected on an image side will be an uniform speed scanning, and the image on the image side will be deviated. Therefore, the laser scanning unit or the MEMS laser scanning unit (MEMS LSU) composed of MEMS reflecting mirrors has a characteristic that scan lights at different angles are formed in the same time interval after the laser beam is scanned by the MEMS reflecting mirror.
As disclosed in U.S. Pat. No. 7,184,187, provided a polynomial surface for fθ lens to adjust the angular velocity variation in the main-scanning direction only. However, the laser light beam is essential an oval-like shape of the cross section that corrects the scan lights in the main-scanning direction only may not be achieve the accuracy requirement. Since, a fθ lens with main-scanning direction correcting as well as sub-scanning direction correcting demands immediate attentions and feasible solutions.